Is there any historical evidence for Caesar Tiberius (commonly referred to Tiberius Caesar) having a co-regency with his predecessor Caesar Augustus? I have read (in a book that I don't remember the title nor author) that some believe there was a co-regency. In an article from Answers In Genesis (see Conclusion), the author writes

[S]ome have postulated a co-regency (joint rule) of Tiberius and Augustus during the last few years of Augustus’s reign. However, there is no reliable ancient historical evidence for such co-regency.

[emphasis mine]

Is there "no reliable ancient historical evidence" for a co-regency of Tiberius and Augustus? Is there any evidence at all?

For a little background, Caesar Augustus was the first Emperor of the Roman Empire. He succeeded the dictator Caesar Julius (commonly referred to as Julius Caesar) and was succeeded by Caesar Tiberius. Some claim Tiberius was co-regent with Augustus for a couple years prior to Augustus' death. A co-regency is the situation where a monarchical position (such as king, queen, emperor or empress), normally held by only a single person, is held by two or more.

The article mentioned is about when Jesus Christ died. I shall explain why a co-regency of Tiberius and Augustus is important to Christian apologetics. Had there been a co-regency, Jesus could have started His ministry as early as AD 26 or 27, allowing for AD 30 to be the date of Jesus' death. Had there been no co-regency, His ministry would have started at about AD 29, putting His death around AD 33.

No, because a Republic does not have a regent. Augustus had powers and honors, but not an office (except when he held traditional offices like consul). After Augustus's death, Tiberius began ending the fiction that Rome was still a Republic.
– C MonsourMay 11 '19 at 14:48

1 Answer
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It depends precisely what is meant by "co-regency". I will try to outline the widely accepted facts.

According to historian Beth Severy, Augustus announced his intention in 4 CE that Tiberius should inherent his title as emperor. Augustus adopted Tiberius as a son and give him a triumph and "a special grant of imperium". Over the following decade:

For the most part, Tiberius led the empire's military campaigns, while Augustus administered the city of Rome. The various problems which arose in this period were handled by both men in a way that reinforced the role of their family in the state.

In 12 CE, there was some sort of ceremony that implied recognition of Tiberius as "co-princep". This is described by Suetonius.

Then according to Wikipedia, after Augustus' death in 14 CE:

The Senate convened on 18 September, to validate Tiberius's position
as Princeps and, as it had done with Augustus before, extend the
powers of the position to him. These proceedings are fully accounted
by Tacitus. Tiberius already had the administrative and political
powers of the Princeps, all he lacked were the titles—Augustus, Pater
Patriae, and the Civic Crown (a crown made from laurel and oak, in
honor of Augustus having saved the lives of Roman citizens).